How limit rotation constraint work?
As far as I understand, a constraint defines a range of allowed values and if the value is outside of it, it snaps to the nearest boundary. Unfortunately it doesn't operate on transform properties, where you can have e.g. 1000° rotation, but on matrices using quaternions.

rotation angles differing precisely by the natural period will be encoded into identical quaternions and recovered angles will be limited to { 0 , 2 π } (in radians)

https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
This means, that for a constraint, 460° angle is the same as 100° (100°+360° = 460°). You can't therefore constrain an object to some number of rotations, after which it will no longer rotate. So if you set the constraints to -180°..180°, it is not constrained at all, because no matrix can translate to a different value in Euler rotation. If an object is at 181° rotation, it is the same as if it was at -179°. Therefore, if you want to limit your object's rotation to 150°..225° range, you have to use two constraints: 150°..180° (any higher value would also work but would really mean 180°), and then -180°..-135° - the problem is, you can't combine constraints like that, they are applied one after another. So if the rotation is 181°, after converting to quaternions and back, it is now -179°, which is below the lower limit of 150°, so it is clamped to the lower limit, unintuitively snapping from 181° to 150° instead of closer 180°:

When the next constrain is applied, it will now snap this angle to the -180°..-135° range.
The general solution is to rotate the object to exactly half its possible rotation and apply rotation to set it to 0, so that now it can move 180 degrees in either direction. In your case, knowing the constrained range is much smaller, you may feel tempted to apply the rotation at a more elegant position, e.g. -45°, since -225° + 45° is exactly -180°, but then you would run into the mentioned flipping problems when a value below -180° suddenly changes to a value below 180° and is snapped to the wrong boundary of the constrain, so remember to give yourself some safety margin.

If you don't want the flipping:

Then you just have to resign from the constraints and use a driver: